Machine Design Distortion Energy Theory for ductile materials

Machine Design Distortion Energy Theory for ductile materials

1. XX/XX/XXXX Distortion-Energy Theory for Ductile Materials

2. Yield point refers to the point at which a material begins to deform permanently under an applied load. Distortion refers to any change in the shape or dimensions of a material or structure due to the application of stress or external forces. Definition of Terms

3. initially developed by Richard von Mises also called von Mises Energy Theory or von Mises- Hencky Theory Distortion-Energy Theory

4. States that “ yielding occurs when the maximum distortion energy is equal to the distortion energy at yielding in a uniaxial tensile test ”. + ] ; = , = =0 + ] + ] ]   Distortion-Energy Theory

5. States that “ yielding occurs when the maximum distortion energy is equal to the distortion energy at yielding in a uniaxial tensile test ”. + ] ; = , = =0 + ] + ] ]   Distortion-Energy Theory

6. + ] = + ] = The term on the left is often called equivalent von Mises stress. If it is larger than the yield strength of the material, yielding is predicted to have occurred.   Distortion-Energy Theory

7. The equivalent von Mises stress is a common output from stress analysis performed using the finite method. Contour plots are typically generated to show the distribution of the von Mises equivalent stress within a component, as these allow areas at risk of yielding to be identified. Distortion-Energy Theory

8. Yield Surface- is the representation of a failure theory in the principal stress space. plane stress case By convention principal stresses are ordered from largest to smallest. plane stress case = 0 If Sigma-C is equal to zero, and so the two axes of yield surface graph correspond the two non-zero principal stresses, Sigma-A and Sigma-B.   Distortion-Energy Theory

9. The yield surface for the Maximum Principal Stress theory. Yielding begins when either of these principal stresses is equal to the yield strength of the material. Distortion-Energy Theory

10. Tresca ( maximum shear stress ) Easier to apply More conservative Von Mises ( maximum distortion energy ) Better agreement with experimental data Distortion-Energy Theory

11. Brittle Materials failure is considered to occur by fracture rather than yielding. brittle materials have compressive strengths that are much larger than their tensile strengths. Distortion-Energy Theory

12. EXAMPLE: The load on a bolt consist of an axial pull of 25 kN together with a transverse shear force of 10 kN. Find the diameter of the bolt required according to maximum distortion-energy theory. Take permissible tensile stress at elastic limit as 120 MPa. Given Data: kN d=? = 120 N/   Distortion-Energy Theory

13. Solution: = = = = Max. Principal stress: =( ; = 0 =( =( =   Distortion-Energy Theory

14. Solution: Min. Principal stress: =( ; = 0 =( =( =   Distortion-Energy Theory

15. Solution: Maximum distortion energy theory = & = =120   Distortion-Energy Theory

16. Solution: =120 d = 18.43   Distortion-Energy Theory

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